What is the general solution for 2tan^2(x)-9tan(x)+7=0 ?

The general solution for 2tan^2(x)-9tan(x)+7=0 is x=1.29249…+pin,x= pi/4+pin

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2tan^2(x)-9tan(x)+7=0

2 tan^{2} (x) - 9 tan (x) + 7 = 0

x = 1.29249 \dots + πn, x = \frac{π}{4} + πn

Solution steps

2 tan^{2} (x) - 9 tan (x) + 7 = 0

Solve by substitution

tan (x) = \frac{7}{2}, tan (x) = 1

tan (x) = \frac{7}{2} : x = arctan (\frac{7}{2}) + πn

tan (x) = 1 : x = \frac{π}{4} + πn

Combine all the solutions

x = arctan (\frac{7}{2}) + πn, x = \frac{π}{4} + πn

Show solutions in decimal form

x = 1.29249 \dots + πn, x = \frac{π}{4} + πn

\frac{1}{2} = cos^{2} (x)

cos (A) = \frac{1}{2}

3 sin^{2} (x) - sin (x) = 0

tan (x) = csc (x)

1 - csc^{2} (\frac{x}{2}) (\frac{1}{2}) = 0

What is the general solution for 2tan^2(x)-9tan(x)+7=0 ?
The general solution for 2tan^2(x)-9tan(x)+7=0 is x=1.29249…+pin,x= pi/4+pin